Synthesis of Single-Case Design Mediation Effects using Two-Stage Multilevel Modeling (Poster 8)

• In Event: Innovative Methodologies and Systematic Reviews in Analyzing Single-Case Experimental Design Data

Abstract

Mediation analysis in Single Case Experimental Designs (SCEDs) allows for evaluating mechanisms through which interventions achieve effects for a single individual. Modeling approaches have been described and empirically validated for mediation analysis in the AB design, however, no study to date has focused on synthesizing indirect effects across participants from a multiple baseline design (MBD). The current study fills the gap by investigating the two-stage multilevel modeling approach using a large-scale Monte Carlo simulation study.
Hierarchical structured SCED data from MBDs across participants were generated assuming that the intervention causes a change in level of the mediator variable, M_(t,j)=α_(0,j)+α_(1,j) 〖Phase〗_(t,j)+ε_(mt,j), and the outcome variable, Y_(t,j)=β_(0,j)+β_(1,j) 〖Phase〗_(t,j)+β_(2,j) M_(t,j)+β_(3,j) 〖Phase〗_(t,j)*M_(t,j)+ε_(yt,j) for each of the J participants. Phaset,j represents the phase variable at time point t where 〖Phase〗_(t,j) = 0 represents the baseline and 〖Phase〗_(t,j) = 1 represents the intervention. Therefore, β_2 × α_1 represents the indirect effect for case J. Next, these coefficients (α_(0,j),α_(1,j),β_(0,j),β_(1,j) β_(2,j)) are allowed to vary between participants within the MBD.
Conditions in the simulation study were designed based on reviews of SCED studies, re-analyses of raw SCED data retrieved from published studies, and previous simulation studies. The total number of measurement occasions was set to 15, 20, 30, or 40 and the number of cases was set to 3, 5, 8, 12, 20, or 28. The true values for the treatment effect for both the mediator variable and the outcome variable were set to 0.00 to 4.00 in 0.50 increments . The strength of the mediator-outcome relation was set to 0 or 0.59 and intervention-mediator interaction was set to 0 or 0.39. Within-case variance was set to 1.00. The between-case variance matrix was manipulated to have conditions with small and large amounts of between-case variance relative to within-case variance. 2,000 datasets were generated per condition.
The simulation was conducted in R. Data were analyzed using the two-stage multilevel approach. At Stage 1 ordinary least squares regression was used to obtain point estimates and standard errors for all coefficients. At Stage 2, a random effects model was fit combining the case-specific estimates of β_2 and α_1 assuming these effects follow a multivariate normal distribution with means corresponding to the fixed effects and covariance matrix corresponding to between-case variances. The average estimates of β_2 and α_1 were multiplied to obtain the indirect effect. Next, β_2 and α_1 and their standard errors were used as input in the RMediation package to get the distribution of the product confidence intervals for the indirect effect. We will evaluate the relative bias of the indirect effect and the coverage, Type 1error rate, and power of confidence intervals for the indirect effect. We are interested in the statistical properties of the two-stage approach so we can recommend under which conditions the method can be applied.
Findings from this study have important implications for the design and statistical analysis in numerous fields that routinely employ SCEDs, ranging from psychology to education and nursing.

Authors

• Mariola Moeyaert, University at Albany - SUNY

• Matthew Valente, University of South Florida

• Milica Miocevic, McGill University

• Sofía Isabel Maiz García, Instituto de Psicoterapia

• Yaosheng Lou, University at Albany - SUNY